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An Experiment on Autoregressive and Threshold Autoregressive Models with Non-Gaussian Error with Application to Realized Volatility

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  • Ziyi Zhang

    (Department of Statistics and Actuarial Science, University of Hong Kong, Hong Kong, China
    Current address: Room C, Front Portion, 2/F, No.425Z Queen’s Road West, Hong Kong.
    These authors contributed equally to this work.)

  • Wai Keung Li

    (Department of Statistics and Actuarial Science, University of Hong Kong, Hong Kong, China
    These authors contributed equally to this work.)

Abstract

This article explores the fitting of Autoregressive (AR) and Threshold AR (TAR) models with a non-Gaussian error structure. This is motivated by the problem of finding a possible probabilistic model for the realized volatility. A Gamma random error is proposed to cater for the non-negativity of the realized volatility. With many good properties, such as consistency even for non-Gaussian errors, the maximum likelihood estimate is applied. Furthermore, a non-gradient numerical Nelder–Mead method for optimization and a penalty method, introduced for the non-negative constraint imposed by the Gamma distribution, are used. In the simulation experiments, the proposed fitting method found the true model with a rather insignificant bias and mean square error (MSE), given the true AR or TAR model. The AR and TAR models with Gamma random error are then tested on empirical realized volatility data of 30 stocks, where one third of the cases are fitted quite well, suggesting that the model may have potential as a supplement for current Gaussian random error models with proper adaptation.

Suggested Citation

  • Ziyi Zhang & Wai Keung Li, 2019. "An Experiment on Autoregressive and Threshold Autoregressive Models with Non-Gaussian Error with Application to Realized Volatility," Economies, MDPI, vol. 7(2), pages 1-11, June.
    • Handle: RePEc:gam:jecomi:v:7:y:2019:i:2:p:58-:d:240654
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    References listed on IDEAS

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    Cited by:

    1. Wing-Keung Wong, 2020. "Editorial Statement and Research Ideas for Efficiency and Anomalies in Stock Markets," Economies, MDPI, vol. 8(1), pages 1-4, February.
    2. Kai-Yin Woo & Chulin Mai & Michael McAleer & Wing-Keung Wong, 2020. "Review on Efficiency and Anomalies in Stock Markets," Economies, MDPI, vol. 8(1), pages 1-51, March.

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